OPTIMIZATION OF NEUMANN EIGENVALUES UNDER CONVEXITY AND GEOMETRIC CONSTRAINTS

Beniamin Bogosel; Antoine Henrot; Marco Michetti

doi:10.1137/24M1641099

OPTIMIZATION OF NEUMANN EIGENVALUES UNDER CONVEXITY AND GEOMETRIC CONSTRAINTS

Beniamin Bogosel
, Antoine Henrot
, Marco Michetti

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we study optimization problems for Neumann eigenvalues μ_k among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, though some results are stated in higher dimension. We study the existence of an optimal domain in all considered cases. We also consider the case of the unit disk, giving values of the index k for which it can or cannot be extremal. We give some numerical examples for small values of k that lead us to state some conjectures.

Original language	English
Pages (from-to)	7327-7349
Number of pages	23
Journal	SIAM Journal on Mathematical Analysis
Volume	56
Issue number	6
DOIs	https://doi.org/10.1137/24M1641099
Publication status	Published - 1 Jan 2024

Keywords

Neumann eigenvalues
convexity
diameter constraint
perimeter contraint
shape optimization

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10.1137/24M1641099

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title = "OPTIMIZATION OF NEUMANN EIGENVALUES UNDER CONVEXITY AND GEOMETRIC CONSTRAINTS",

abstract = "In this paper we study optimization problems for Neumann eigenvalues μk among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, though some results are stated in higher dimension. We study the existence of an optimal domain in all considered cases. We also consider the case of the unit disk, giving values of the index k for which it can or cannot be extremal. We give some numerical examples for small values of k that lead us to state some conjectures.",

keywords = "Neumann eigenvalues, convexity, diameter constraint, perimeter contraint, shape optimization",

author = "Beniamin Bogosel and Antoine Henrot and Marco Michetti",

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N2 - In this paper we study optimization problems for Neumann eigenvalues μk among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, though some results are stated in higher dimension. We study the existence of an optimal domain in all considered cases. We also consider the case of the unit disk, giving values of the index k for which it can or cannot be extremal. We give some numerical examples for small values of k that lead us to state some conjectures.

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KW - Neumann eigenvalues

KW - convexity

KW - diameter constraint

KW - perimeter contraint

KW - shape optimization

UR - https://www.scopus.com/pages/publications/85209223610

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JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -

OPTIMIZATION OF NEUMANN EIGENVALUES UNDER CONVEXITY AND GEOMETRIC CONSTRAINTS

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Keywords

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